JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(a, b\), c be three distinct real numbers, none equal to one. If the vectors \(a \hat{i}+\hat{j}+\hat{k}, \hat{i}+b \hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+ c \hat{k}\) are coplanar, then \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}\) is equal to
- A \(1\)
- B \(-1\)
- C \(-2\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right|=0\) \(C _2 \rightarrow C _2- C _1, C _3 \rightarrow C _3- C _1\) \(\left|\begin{array}{lll}a & 1-a & 1-a \\ 1 & b -1 & 0 \\ 1 & 0 & c -1\end{array}\right|=0\) \(a(b-1)(c-1)-(1-a)(c-1)+(1-a)(1-b)=0\)…
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